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  1. Abstract

    We revisit the linear boundary‐layer approximation that expresses a generalized Ekman balance and use it to clarify a range of interpretations in the previous literature on the tropical cyclone boundary layer. Some of these interpretations relate to the reasons for inflow in the boundary layer and others relate to the presumed effects of inertial stability on boundary‐layer dynamics. Inertial stability has been invoked, for example, to explain aspects of boundary‐layer behaviour, including the frontogenetic nature of the boundary layer and its relationship to vortex spin‐up. Our analysis exposes the fallacy of invoking inertial stability as a resistance to radial inflow in the boundary layer. The analysis shows also that the nonlinear acceleration terms become comparable to the linear Coriolis acceleration terms in relatively narrow vortices that are inertially stable above the boundary layer. Estimates of the nonlinear accelerations using the linear solutions are expected to underestimate the actual contribution in a nonlinear boundary‐layer model, cautioning against neglecting the nonlinear terms in diagnostic or prognostic models.

     
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  2. Abstract

    An idealized, three‐dimensional, 1 km horizontal grid spacing numerical simulation of a rapidly intensifying tropical cyclone is used to extend basic knowledge on the role of mean and eddy momentum transfer on the dynamics of the intensification process. Examination of terms in the tangential and radial velocity tendency equations provides an improved quantitative understanding of the dynamics of the spin‐up process within the inner‐core boundary layer and eyewall regions of the system‐scale vortex. Unbalanced and non‐axisymmetric processes are prominent features of the rapid spin‐up process. In particular, the wind asymmetries, associated in part with the asymmetric deep convection, make a substantive contribution (30%) to the maximum wind speed inside the radius of this maximum. The analysis provides a novel explanation for inflow jets sandwiching the upper‐tropospheric outflow layer which are frequently found in numerical model simulations. In addition, it provides an opportunity to assess the applicability of generalized Ekman balance during rapid vortex spin‐up. The maximum tangential wind occurs within and near the top of the frictional inflow layer and as much as 10 km inside the maximum gradient wind. Spin‐up in the friction layer is accompanied by supergradient winds that exceed the gradient wind by up to 20%. Overall, the results affirm prior work pointing to significant limitations of a purely axisymmetric balance description, for example, gradient balance/Ekman balance, when applied to a rapidly intensifying tropical cyclone.

     
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  3. Abstract

    Tropical cyclone formation and evolution at, or near, the Equator is explored using idealized three‐dimensional model simulations, starting from a prescribed, initial, weak counterclockwise rotating vortex in an otherwise quiescent,nonrotatingenvironment. Three simulations are carried out in which the maximum tangential wind speed (5 m s) is specified at an initial radius of 50, 100, or 150 km. After a period of gestation lasting between 30 and 60 hr, the vortices intensify rapidly, the evolution being similar to that for vortices away from the Equator. In particular, the larger the initial vortex size, the longer the gestation period, the larger the maximum intensity attained, and the longer the vortex lifetime. Beyond a few days, the vortices decay as the cyclonic vorticity source provided by the initial vortex is depleted and negative vorticity surrounding the vortex core is drawn inwards by the convectively driven overturning circulation. In these negative vorticity regions, the flow is inertially/centrifugally unstable. The vortex evolution during the mature and decay phases differs from that in simulations away from the Equator, where inertially unstable regions are much more limited in area. Vortex decay in the simulations appears to be related intimately to the development of inertial instability, which is accompanied by an outward‐propagating band of deep convection. The degree to which this band of deep convection is realistic is unknown.

     
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  4. We present idealized, three‐dimensional, convection‐permitting numerical experiments to evaluate the premise of the revised theory of tropical cyclone intensification proposed by Emanuel, . The premise is that small‐scale turbulence in the upper tropospheric outflow layer determines the thermal stratification of the outflow and, in turn, an amplification of the system‐scale tangential wind field above the boundary layer. The aim of our article is to test whether parametrized small‐scale turbulence in the outflow region of a developing storm is an essential process in the spin‐up of the maximum tangential winds.

    Compared with the control experiment, in which the small‐scale, shear‐stratified turbulence is parametrized in the usual way based on a Richardson number criterion, the vortex in a calculation without a parametrized representation of vertical mixing above the boundary layer has similar evolution of intensity. Richardson number near‐criticality is found mainly in the upper‐level outflow. However, the present solutions indicate that eddy processes in the eyewall play a significant role in determining the structure of moist entropy surfaces in the upper‐level outflow. In the three‐dimensional model, these eddy processes are largely realizations of asymmetric deep convection and are not obviously governed by any Richardson‐number‐based criterion. The experiments do not support the premise on which the new theory is based. The results would appear to have ramifications for recent studies that invoke the new theory.

     
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  5. Analyses of dropsonde data collected in HurricaneEdouard(2014) just after its mature stage are presented. These data have unprecedentedly high spatial resolution, based on 87 dropsondes released by the unmanned NASA Global Hawk from an altitude of 18 km during the Hurricane and Severe Storm Sentinel (HS3) field campaign. Attempts are made to relate the analyses of the data to theories of tropical cyclone structure and behaviour. The tangential wind and thermal fields show the classical structure of a warm‐core vortex, in this case with a secondary eyewall feature. Additionally, the equivalent potential temperature field (θe) shows the expected structure with a mid‐tropospheric minimum at outer radii and contours ofθeflaring upwards and outwards at inner radii. With some imagination, these contours are roughly congruent to the surfaces of absolute angular momentum. However, details of the analysed radial velocity field are quite sensitive to the way in which the sonde data are partitioned to produce an azimuthal average. This sensitivity is compounded by an apparent limitation of the assumed steadiness of the storm over the period of data collection.

     
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  6. Many previous diagnoses of the global kinetic energy budget for a tropical cyclone have given prominence to the global integral of a pressure–work term in the generation of kinetic energy. However, in his erudite textbookAtmosphere–Ocean Dynamics, Adrian Gill derives a form of the kinetic energy equation in which there is no such explicit source term. In this article we revisit the interpretations of the generation of kinetic energy given previously in light of Gill's analysis and compare the various interpretations, which are non‐unique. Further, although global energetics provide a constraint on the flow evolution, in the context of the kinetic energy equation they conceal important aspects of energy generation and consumption, a finding which highlights the limitations of a global kinetic energy budget in revealing the underlying dynamics of tropical cyclones.

     
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